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One expected outcome of physics instruction is that students develop quantitative reasoning skills, including strategies for evaluating solutions to problems. Examples of well-known “canonical” evaluation strategies include special case analysis, unit analysis, and checking for reasonable numbers. We report on responses from three tasks in different physics contexts prompting students in an introductory calculus-based physics sequence to evaluate expressions for various quantities: the velocity of a block at the bottom of an incline with friction, the final velocities of two masses involved in an elastic collision, and the electric field due to three point charges. Responses from written ( $\mathit{N}=580$) and interview ( $\mathit{N}=18$) data were analyzed using modified grounded theory and phenomenology. We also employed the analytical framework of epistemic frames. Students’ evaluation strategies were classified into three broad categories: consulting external sources, checking through computation, and comparing to the physical world. Some of the evaluation strategies observed in our data, including canonical as well as noncanonical strategies, have been reported in prior research on evaluation, albeit sometimes with different names and with varying levels of generalizability. We note four major, general observations prompted by our results. First, most students did not evaluate solutions to physics problems using an approach that an expert would consider an evaluation strategy. Second, many students used evaluation strategies that emphasized computation. Third, many students used evaluation strategies that are not canonical but are nonetheless useful. Fourth, the relative prevalence of different strategies was highly dependent on the task context. We conclude with remarks including implications for classroom instruction. 

Physics students are introduced to vector fields in introductory courses, typically in the contexts of electric and magnetic fields. Vector calculus provides several ways to describe how vector fields vary in space including the gradient, divergence, and curl. Physics majors use vector calculus extensively in a junior-level electricity and magnetism (E&M) course. Our focus here is exploring student reasoning with the partial derivatives that constitute divergence and curl in vector field representations, adding to the current understanding of how students reason with derivatives. 

This work is part of a broader project to investigate student understanding of mathematical ideas used in upper-division physics. This study in particular probes students’ understanding of the divergence and curl operators as applied to vector field diagrams. We examined how students reason with partial derivatives that constitute divergence and curl of the vector field diagrams. Students’ written responses to a task on derivatives, divergence, and curl of a 2D vector field were collected and coded. Students were generally successful in determining the sign of some of the constituent derivatives of div and curl, but struggled in one case in which components were negative. Analysis of written explanations showed confusion between the sign, direction, and change in the magnitude of vector field components.